Am 08.11.2013 19:10, schrieb Bart Goddard: > Timothy Murphy <firstname.lastname@example.org> wrote in news:l5dg9v$tn6$1@dont- > email.me: > >> It's clear that the upper limit is 1, >> since n pi mod Z will be distributed evenly in [0,1), >> and so will infinitely often be in the range (1/3,2/3). > > I don't think this is true. |Sin(n)| is probably > distributed evenly, but raising to (1/n) power is going > to crowd things toward 0. >
That' a misconception. Its wrong the microscopic view for positive numbers < 1.
The n-th root, n large positive integer, concentrates all positive numbers toward 1, because x^(1/n) and 1/x^(1/n)=(1/x)^(1/n) are inverses of each other.